Home
Class 12
MATHS
The number of elements in the domain of ...

The number of elements in the domain of the function `f(x)=sin^(-1)((x^2-2x)/3)+sqrt(([x]+[-x]))` , (where [.] denotes the greater integer function) is equal to a. 4 b. 6 c. 3 d. 5

A

6

B

4

C

3

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=sin^(-1)((x^(2)-2x)/(3))+sqrt([x]+[-x])`
`sin^(-1)((x^(2)-2x)/(3))"is denfined for"-1le(x^(2)-2x)/(3)le1`
and `sqrt([x]-[-x])` is defined only for integral values of x
`rArr" "x=-1,0,1,2,3`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|9 Videos

  • FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE ENGLISH|Exercise DPP 3.4|14 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE ENGLISH|Exercise Exercises 1.18|1 Videos

Similar Questions

Explore conceptually related problems

Find the domain of the function f(x)=sin^(-1)(2x-3)

Find the domain of the function f(x)=sin^(-1)(2x-3) .

f(x)=1/sqrt([x]^(2)-[x]-6) , where [*] denotes the greatest integer function.

The domain of the function f(x)=log_e {sgn(9-x^2)}+sqrt([x]^3-4[x]) (where [] represents the greatest integer function is

The domain of the function f(x)=(1)/(sqrt([x]^(2)-[x]-20)) is (where, [.] represents the greatest integer function)

The domain of the function f(x)=log_(3)log_(1//3)(x^(2)+10x+25)+(1)/([x]+5) (where [.] denotes the greatest integer function) is

The domain of the function f(x)=(sin^(-1)(3-x))/("In"(|x|-2)) is

The number of elements in the range of functions: y=sin^(-1) [x^(2)+5/9]+cos^(-1) [x^(2)-4/9] where where [.] denotes the greatest integer function is:

The domain of the function f(x)=(1)/(sqrt((x)-[x])) where [*] denotes the greatest integer function is

Domain of the function f(x) = sin^(-1) [1 + cos x]- sqrt(16-x^(2)) ([.) denotes the greatest integer function) is